Understanding the behavior of a system's output is fundamental in many fields, including engineering and control theory. The question asks about the characteristic of a system whose output remains "under control".

System Output and Control

When we say a system's output is 'under control', it generally means that the output signal does not grow without bound over time. Instead, it remains within certain limits or settles to a specific value, even when disturbances are applied or when the system is given an input.

Defining a Stable System

A system is considered stable if, for any bounded input, its output is also bounded. In simpler terms, if you give a stable system an input that doesn't go to infinity, its output won't go to infinity either. This is precisely what is meant by the output being 'under control'. A stable system's response remains within limits.

Let's consider the other options:

• Unstable: An unstable system is the opposite of a stable system. For a bounded input, the output of an unstable system grows without bound. This means the output is definitely not under control.
• Constant: A constant output is a specific type of output, but it's not the definition of 'under control'. A system can have a non-constant but still bounded and controlled output (e.g., oscillating within limits or settling to a non-zero value). A constant output is a special case that occurs under certain conditions in a stable system (like steady-state response to a constant input).
• Flexible: Flexibility typically refers to a system's ability to adapt or handle variations in inputs or conditions. While a flexible system might be designed to handle a range of operations, this term does not directly describe whether its output remains bounded or 'under control' in the technical sense of stability.

Therefore, a system whose output is under control is best described as a stable system because stability guarantees that the output remains bounded and does not run away to infinity, keeping it manageable and 'under control'.